A search for the leptonic charge asymmetry (A'c) of top-quark-antiquark pair production in association with a W boson (t-tW) is presented. The search is performed using final states with exactly three charged light leptons (electrons or muons) and is based on p s = 13TeV proton-proton collision data collected with the ATLAS detector at the Large Hadron
Collider at CERN during the years 2015-2018, corresponding to an integrated luminosity of 139 fb-1. A profile-likelihood fit to the event yields in multiple regions corresponding to positive and negative differences between the pseudorapidities of the charged leptons from top-quark and top-antiquark decays is used to extract the charge asymmetry. At reconstruction level, the asymmetry is found to be -0.12 +- 0.14 (stat.) +-0.05 (syst.).
An unfolding procedure is applied to convert the result at reconstruction level into a charge-asymmetry value in a fiducial volume at particle level with the result of -0.11 +- 0.17 (stat.) +-0.05 (syst.). The Standard Model expectations for these two observables are calculated using Monte Carlo simulations with next-to-leading-order plus parton shower precision in quantum chromodynamics and including next-to-leading-order electroweak corrections. They are -0.084 +0.005
-0.003 (scale) +-0.006 (MC stat.) and -0.063 +0.007
-0.004 (scale)
+-0.004 (MC stat.) respectively, and in agreement with the measurements.